(2x2+10x+12)/2=72

Solution for (2x2+10x+12)/2=72 equation:

(2x^2+10x+12)/2=72

We move all terms to the left:

(2x^2+10x+12)/2-(72)=0

We multiply all the terms by the denominator


(2x^2+10x+12)-72*2=0

We add all the numbers together, and all the variables

(2x^2+10x+12)-144=0

We get rid of parentheses

2x^2+10x+12-144=0

We add all the numbers together, and all the variables

2x^2+10x-132=0

a = 2; b = 10; c = -132;
Δ = b2-4ac
Δ = 102-4·2·(-132)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-34}{2*2}=\frac{-44}{4}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+34}{2*2}=\frac{24}{4}
=6
$